To this aim we recall definition of this notion below, [1]}, Chapter IX.

We say that \(\lbrace U_A(z)\rbrace _{z\in S_\theta }\) , is a holomorphic contraction semigroup
with generator \(A \in {H}_{c}(\theta ,0)\) , if its restriction
\(\lbrace U_A(t)\rbrace _{t \ge 0}\)  to \({{\mathbb {R}}}^{+}_0\)  is a contraction \(C_0\) -semigroup, that is
\({H}_{c}(\theta , 0):= {H}(\theta , 0) \cap {G}(1,0)\) .
